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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

Henri Poincare

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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
Astronomer
Engineer
Mathematician
Philosopher
Philosopher Of Science
Physicist
Researcher
Topologist
University Teacher
Le Cateau
Jules Henri Poincaré
Poincaré
Henri Poincare
Jules Henri Poincare
Poincare
Feeling
Feelings
Idaho
Giving
Demonstration
Elegance
Solution
Solutions
Indeed
Gives

More quotes by Henri Poincare

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It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.
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Thought is only a flash between two long nights, but this flash is everything.
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Mathematical discoveries, small or great are never born of spontaneous generation.
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If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.
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Point set topology is a disease from which the human race will soon recover.
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Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.
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All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.
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What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them it is that which satisfies the rules of logic. But in education it is not that it is one that can be understood by the pupils.
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Les faits ne parlent pas. Facts do not speak.
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A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.
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But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.
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Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
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The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.
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Mathematics is the art of giving the same name to different things.
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It is far better to foresee even without certainty than not to foresee at all.
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The mind uses its faculty for creativity only when experience forces it to do so.
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It is through science that we prove, but through intuition that we discover.
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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
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